Which of the following is NOT a correct mathe | vedclass

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(D) For a weak electrolyte $HA \rightleftharpoons H^{+} + A^{-}$,the dissociation constant $K_{a}$ is given by $K_{a} = \frac{C\alpha^2}{1-\alpha}$.As

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$\alpha = \sqrt{\frac{K_{a}}{V}}$

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(D) For a weak electrolyte $HA \rightleftharpoons H^{+} + A^{-}$,the dissociation constant $K_{a}$ is given by $K_{a} = \frac{C\alpha^2}{1-\alpha}$.Assuming $\alpha \ll 1$,we have $K_{a} \approx C\alpha^2$.From this,$\alpha = \sqrt{\frac{K_{a}}{C}}$.Since concentration $C = \frac{1}{V}$,where $V$ is the volume,we can substitute $C$ to get $K_{a} = \frac{\alpha^2}{V}$ or $\alpha = \sqrt{K_{a}V}$.Comparing these with the given options:Option $A$ is $\alpha = \sqrt{\frac{K_{a}}{C}}$ (Correct).Option $B$ is $K = \frac{\alpha^2}{V}$ (Correct).Option $C$ is $K = \alpha^2 C$ (Correct,as $K = C\alpha^2$).Option $D$ is $\alpha = \sqrt{\frac{K_{a}}{V}}$,which is incorrect because $\alpha = \sqrt{K_{a}V}$.

Which of the following is $NOT$ a correct mathematical equation for Ostwald dilution law?

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